Surprisingly it's not that much. At a constant 1G acceleration you could travel across the galaxy (100k light years) in 12 years (from your reference frame)[0].

I definitely agree that such travel would require enormous amounts of energy.

[0]: https://en.wikipedia.org/wiki/Space_travel_under_constant_ac...

also, "instantaneously" is a stretch on a galactic scale. 299792000 m/s isn't as fast as it sounds if you need to cross the entire galaxy.

Time dilation doesn't matter here.